Specifying button display ordering in the Brightcove player.

custom-control.css

/* Specify where your custom control should show up relative to the other buttons.
   Buttons are displayed in ascending order, from left to right. The CSS spec only 
   requires `order` today but you should include the other rules so that your button
   is placed correctly on older browsers. 
*/
.video-js .vjs-custom-control {
  order: 5; /* after the progress bar but before the volume button */
  -webkit-box-ordinal-group: 5;
  -moz-box-ordinal-group: 5;
  -webkit-order: 5;
  -ms-flex-order: 5;
}